Fractional‐order filter‐based enhanced full state feedback control design with multi‐objective formulation using grey wolf optimization algorithm

Abstract

A perturbed fractional-order filter (FOF)-based LQR control design with multiple performance indices is proposed in this paper. Three variants of the FOF-based linear quadratic regulator (LQR) system have been proposed along with choices on the commensurate order of state feedback law. The multi-objective problem formulation has been done with three performance objectives to address the different issues of design. The first performance index constitutes a weighted sum of ITAE (Integral Time of Absolute Error) and the difference between the eigenvalues of the plant and the LQR controlled plant, chosen to minimize the large oscillations as well as relative stability with respect to eigenvalues. A new lower bound of the singular values have been addressed to ensure the robust stability of the system through the formulation of a second performance objective. It is the minimization of singular values of the return ratio matrix at the plant's input. The third and the last performance index aims minimization of maximum singular values of the perturbation transfer function at the plant's output, so as to guarantee no closed-loop right half plane zeros. The multi-objective optimization problem is solved and the optimal solutions are obtained via Grey Wolf Optimization Algorithm. The simulation results validate the performance and effectiveness of the proposed control design.